The **Dagum distribution** (also called the *Inverse Burr distribution*; Dagum called it the *generalized logistic-Burr distribution*) was proposed by Camilo Dagum in the 1970s to model income and wealth distribution. Dagum developed the models as an alternative to the Pareto Distribution and lognormal distribution, which he felt didn’t result in accurate models when applied to spread of income.

Dagum wasn’t satisfied with how the Pareto and lognormal distributions handles **heavy-tailed data**. Specifically, he felt a better model could be developed for the heavy tails often found in empirical income and wealth distributions, while allowing for an **interior mode**. The Pareto handles heavy tails well, but the lognormal does not. And while the lognormal allows an interior mode (or a mode at zero), the Pareto doesn’t. Dagum’s distribution allows for an interior mode *and *it handles heavy tails (Kleiber, 2007).

Despite its relative unpopularity, the Dagum distribution **often performs better **than other two/three parameter income/wealth distribution models when applied to empirical data.

## Dagum Distribution CDF and PDF

The CDF of the Type I (three parameter) Dagum distribution is:

And the PDF is:

Where:

- λ = a scale parameter,
- δ and Β = shape parameters.

When Β = 1, the distribution is called the log-logistic distribution.

## Types

The three parameter **Dagum Type I distribution** evolved from Dagum’s experimentation with a shifted log-logistic distribution (Chotikapanich, 2008). Two four-parameter (Type II) generalizations were also developed.

## References

Atkinson, A. (2014). Handbook of Income Distribution, Volume 2. Elsevier.

Chotikapanich, D. (Ed.) (2008). Modeling Income Distributions and Lorenz Curves. Springer Science & Business Media.

Dagum, C., A New Model of Personal Income Distribution: Specification and Estimation,

Economie Applique’e, 30, 413 – 437, (1977).

Kleiber, C. & Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. John Wiley & Sons.

Kleiber, C. (2007). A Guide to the Dagum Distributions. Retrieved May 26, 2020 from: http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=BEE8C9083715B6042596B0DC170BFDA1?doi=10.1.1.610.8346&rep=rep1&type=pdf

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